Question

Joe measured the diameter of a tennis ball correct to the nearest millimetre. The upper bound of his measurement was 6.75 centimetres. Write down, in imillimetres, the lower bound of his measurement.​

Answer 1

The lower bound of the measurement is 65.5 millimetres.

A centimetre equals 10 millimetres, a measure is expressed by the measured magnitude plus uncertainty, the latter one represents the grade of precision of the measure instrument. That is to say:

$y = x + \epsilon$ (1)

Where:

• $x$ - Measured magnitude, in millimeters.
• $y$ - Possible magnitude, in millimeters.
• $\epsilon$ - Uncertainty, in millimeters.

If we know that $y = 67.5\,mm$ and $\epsilon = 1\,mm$, then the lower bound of the measurement is:

$y = 67.5\,mm - 2\cdot (1\,mm)$

$y = 65.5\,mm$

The lower bound of the measurement is 65.5 millimeters.

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